(CNN) -- A California judge ruled Monday that a then 10-year-old boy committed second-degree murder -- and knew what he was doing was wrong -- when he fatally shot his father, a local neo-Nazi leader.

Jeffrey Hall was asleep on a couch in his family's Riverside home when his son killed him on May 1, 2011, according to authorities. CNN is not naming the boy, who is now 12, because he is a juvenile.

Hall had been the Southwestern states regional director for the National Socialist Movement, according to an online tribute to him from the group's leader, Jeff Schoep. One of the nation's biggest, most well-known neo-Nazi organizations, the National Socialist Movement idolizes Adolf Hitler and touts virulent rhetoric against those who are Jewish, immigrants and not "pure-blood whites," according to the Southern Poverty Law Center civil rights group.

Prosecutors contend the victim's neo-Nazi background is not linked to his death, saying the young killer's concerns about abuse and his family being split up were more significant factors.

"It was our belief that this would have happened even if (Hall) was not part of the National Socialist Movement," said John Hall, a spokesman for the Riverside County district attorney's office. "This was done more on a domestic level."

According to an arrest warrant issued for Hall's wife, Krista McCary, and posted from the Southern California Public Radio's website, Riverside police arrived in May 2011 at what they described as a "filthy," unkempt home and found the victim dead on the coach "with a gunshot wound to the left side of his head."

Five children -- ages 10, 9, 7, 3 and a 2-month old -- were inside the home at the time, as was McCary, the warrant said.

Three of the children later told a detective they knew where guns were inside the house, according to the arrest warrant. The eldest said he'd taken a revolver off a low shelf in his father's and stepmother's closet, then killed his sleeping father.

The boy told police "he was tired of his dad hitting him and his mom," and that he thought his father was having an affair that might contribute to the family's break-up.

Less than three weeks after Hall's death, McCary was arrested and charged with five counts of willful child endangerment and four counts of criminal storage of a firearm, according to Riverside Superior Court records. In August 2011, she pleaded guilty to one count of each charge and was sentenced to 120 days in custody (all but two of them in work release) and four years of probation.

The boy has been detained in juvenile halls in Riverside County since the shooting. His lawyers initially sought an insanity defense but later dropped that approach and argued their client didn't fully grasp the ramifications of what he did, according to John Hall, the district attorney's spokesman.

The murder trial before county Judge Jean Leonard -- and not a jury -- got underway October 30, 2012, continuing off-and-on for about 10 days over four months, ending Monday.

As there are no "guilty" or "not guilty" verdicts in her California juvenile court, Leonard instead found it "true" that the boy had committed murder and understood his actions were wrong.

The next hearing in the case is scheduled for February 15, where placement of the boy will be determined. The convicted boy could remain in custody up until his 23rd birthday, though he could be freed sooner or have a number of other living arrangements as determined by the judge, said John Hall.

Schoep recalled the 32-year-old victim -- pictured on the tribute website raising a National Socialist Movement flag, which contains a swastika -- as a "dedicated father" who "spent countless hours on the California and Arizona border leading patrols in efforts to halt illegal immigration, (and organized) events for the NSM countless times." Schoep's ex-wife Joanna told the Southern Poverty Law Center that Hall was her ex-husband's best friend.

The same civil rights group described Jeff Hall as "something of a rising star in the neo-Nazi universe." A public advocate for a "white nation," he led rallies full of white supremacists giving Nazi salutes at a day-laborer center and synagogues, in addition to his border patrol activities, according to the law center.

He was also a politician of sorts, earning nearly 30% of the vote -- after he'd publicly stood by his neo-Nazi views -- in a race to join the Western Municipal Water District board of directors in Riverside County.